So how ancient is the obviously sacred and venerable Mughrabi ramp/bridge? Was it built in the time of Mohammed, or during the Mamluk period? Did Yasir Arafat ever step foot on it?
Of course not. It was built in 2007, by Israel, after the earlier ramp collapsed in 2004 in a landslide due to an earthquake and snowstorms that year.
When the ramp collapsed in 2004, the Muslims blamed Israel, saying that Israel was attempting to destroy the entire Temple Mount.
When Israeli archaeologists, after three years of study, announced the collapse had revealed a heretofore unknown ancient Muslim prayer room, Muslims complained that Israel hid this information from them. (How that helps Judaize Jerusalem is an open question.)
And when the temporary ramp was being constructed in 2007, Muslims rioted
Let's go back in time a little. When was the Mughrabi gate re-opened to begin with?
Before 1920, The Mughrabi Gate was closed. At the time the Western Wall was a small cul-de-sac where worshipers could gather in relative privacy. But then the infamous Mufti of Jerusalem opened up the Mughrabi Gate - specifically to turn the area into a thoroughfare so that the Jewish worshipers would be disturbed. They even drove mules through the prayer area.
A few days before the 1929 anti-Jewish pogrom broke out, "an incited Muslim mob rampaged through the opening torn by the Mufti in the south of the plaza, attacking the Jewish worshipers and destroying ritual objects."
(The Mughrabi Gate itself was built only around the 12th century - above what is known as Barclay's Gate, which is believed to be one of the original Second Temple gates. Barclay's Gate was closed off by Muslims in the 10th century and was rediscovered by James Barclay in 1848. It can be seen in the women's section of the Wall today.)
So the Muslims are upset when the ramp collapses, they are upset when Israel builds a temporary replacement, they are upset when Israel closes the temporary replacement ramp.
Keep in mind also that Mughrabi Gate is the only gate that non-Muslims may use to access the Temple Mount. Muslims are not at all inconvenienced by the closure of the ramp - but Jews and Christians are.